This paper presents a complete characterization of shortest paths for unicycle-like nonholonomic mobile robots equipped with a pinhole camera rigidly fixed with limited Field-Of-View (FOV). We preliminarily provide an alphabet of optimal control words and then we demonstrate how to obtain the partition induced by shortest path in the vehicle plane. The word univocally associated to a region encodes the shortest path from any starting point in that region to the goal point of the mobile robot without violating the FOV constraints.